Ab initio melting temperatures of bcc and hcp iron under the Earth's inner core condition

There has been a long debate on the stable phase of iron under the Earth's inner core conditions. Due to the solid-liquid coexistence at the inner core boundary, the thermodynamic stability of solid phases directly relates to their melting temperatures, which remains considerable uncertainty. In the present study, we utilized a semi-empirical potential fitted to high-temperature ab initio data to perform a thermodynamic integration from classical systems described by this potential to ab initio systems. This method provides a smooth path for the thermodynamic integration and significantly reduces the uncertainty of determining the melting temperatures caused by the finite size effect down to 15 K. Our results suggest the hcp phase is the ground state of pure iron under the inner core conditions, while the free energy difference between the hcp and bcc phases is tiny, on the order of 10s meV/atom. It suggests the effect of nickel and light elements must be taken into account to get a complete picture of the crystalline structure of the solid inner core phase.